1 903.] Electric Waves round a Conducting Obstacle. 61 



whence 



that is 



9(n) 



or 



\) = ~ ^3 Y ~ 



Hence 



1 



S- - 8 



/2K C0s(<,,+ Xn) ,. _ 



that is 



or 



COS (</> -*- 



Now for values of ( = cos~V) which are not near to or TT, P n 

 may be replaced by \f -" cos-| (?< + i)0- r > for large values of n; 



TTtl L 4 J 



further, for values of n small compared with r, neglecting small quan- 

 tities, \n is zero and R,, (s) is unity. Hence 



S = - - - 2 w (?t + 1) (2/i +1) {? (x/'i) - t u (K/-!) } { 1 - R n (z) cos XnC iXn } 



9CTi^ 



where is large, but not comparable with ^. Since is not small, 

 *?'! may be replaced by c, and then 





cos x. . 



